skip to main content

Title: An enriched finite element model with q-refinement for radiative boundary layers in glass cooling

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method ismore » analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.« less
Authors:
 [1] ; ;  [2] ;  [1]
  1. Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)
  2. School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom)
Publication Date:
OSTI Identifier:
22230861
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 258; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; BOUNDARY LAYERS; COMPARATIVE EVALUATIONS; EQUATIONS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; GLASS; HEAT TRANSFER; RADIATIVE COOLING; REDUCTION